Fixed points of commutative Lüders operations. (English) Zbl 1201.81008
Summary: This paper verifies a conjecture posed in a pair of papers on the fixed point sets for a class of quantum operations. Specifically, it is proved that if a quantum operation has mutually commuting operation elements that are effects forming a resolution of the identity, then the fixed point set of the quantum operation is exactly the commutant of the operation elements.
MSC:
| 81P15 | Quantum measurement theory, state operations, state preparations |
| 46L07 | Operator spaces and completely bounded maps |
| 47L90 | Applications of operator algebras to the sciences |
| 81R15 | Operator algebra methods applied to problems in quantum theory |
| 47B65 | Positive linear operators and order-bounded operators |
